COM in Collision and Explosion

Q. The first law of motion can be derived from the second law of motion if the mass isand the net external force is.

1. constant
2. zero
3. varying
4. non-zero

Q. Two blocks of masses 5 kg and 2kg are connected by a spring of negilible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 7 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is

Q.

A projectile is fired at a speed of 100 m/s at an angle of ${37}^{\circ }$ above the horizontal. At the highest point, the projectile breaks into two parts of mass in ratio 1 : 3, the smaller coming to rest. Find the distance from the launching point to the point where the heavier piece lands.

1. 1020 m

2. 920 m

3. 1220 m

4. 1120 m

Q. A bullet of mass 40g is fired from a gun of mass 10kg. If the velocity of bullet is 400m/s, then the recoill velocity of the gun is _?

Q. An explosion breaks a rock into three parts. Two pieces go off at right angles to each other with 1.0 kg piece with a velocity of 12 m/s and other 2.0 kg piece with a velocity of 8 m/s. If the third piece flies off with a velocity of 40 m/s, compute the mass of the third piece.

1. 0.5 kg
2. 3 kg
3. 0.7 kg
4. 0.25kg

Q. A gun of mass 4 kg fires a bullet of mass 20 g with a velocity of 50 m/s, recoil velocity of the gun is

1. 25 m/s
2. 0.25 m/s
3. 15 m/s
4. 0.15 m/s

Q. When the speed of an object is doubled, its momentum will be:

1. Quadrupled
2. Same
3. Halved
4. Doubled

Q.

Figure shows a small block of mass 'm' which is started with a speed 'v' on the horizontal part of the bigger block of mass 'M' placed on a horizontal floor. The curved part of the surface shown is semicircular. All the surfaces are frictionless. Find the speed of the bigger block when the smaller block reaches the point A of the surface.

1. towards left

2. towards left

3. towards left

4. towards left

Q. a bullet of mass 10 gram travelling horizontally with a velocity of 160m/s strikes a stationary wooden block and comes to rest in 0.02 seconds. the distance of penetration of the bullet into the block will be 1. 1.20m 2. 1.60m 3. 2.00m 4. 2.40m

Q. A particle of mass 1 kg is projected upwards with velocity 60 m/s. Another particle of mass 2 kg is just dropped from a certain height. Find out the acceleration and the velocity of COM after 2 s when neither of the particles has collided with the ground.

1. $-5m/s^2,60m/s$
2. $-10m/s^2,20m/s$
3. $-10m/s^2,30m/s$
4. $-5m/s^2,20m/s$

Q.

In the figure below the card is flicked with a push. It was observed that the card moves ahead while coin falls in glass.
(ii). Name the law involved in this case.

1. Newton’s First Law of Motion

2. Newton’s Third Law of Motion

3. Law of conservation of Momentum

4. Newton’s Second Law of Motion

Q.

Explain, why an inflated balloon lying on the surface of a floor moves forward when pierced with a needle.

Q.

State Newton's second law. Prove that Newton's first law of motion is contained in Newton's second law

Q.

Two bodies A and B of mases m and 2m respectively are placed on a smooth floor. They are connected by a spring. A third body C of mass m moves with velocity $v_0$ along the line joining A and B and collides elastically with A as shown in figure. At a certain instant of time $t_0$ after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be $x_0$. Determine (a) the common velocity of A and B at time $t_0$ and (b) the spring constant.

1. $v=\frac{v_0}{3},k=\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

2. $v=\frac{v_0}{3},k=\frac{3}{4}\frac{m{v}_0^2}{x_0^2}$

3. $v=\frac{v_0}{2},k=\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

4. $v=\frac{v_0}{2},k=\frac{3}{4}\frac{m{v}_0^2}{x_0^2}$

Q.

A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

1. 50%

2. 56%

3. 62%

4. 44%

Q.

This question has statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement I A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f\left(\frac{1}{2}m{v}^2\right),thenf=(\frac{m}{M}+m)$ Assertion and Reason

1. If Statement I is true, Statement II it true; Statement II is the correct explanation for Statement I

2. If Statement I is false; Statement II is true

3. If Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

4. If Statement I is true; Statement II is false

Q.

A body starts from rest and falls vertically from a height of 19.6 meters. If g=9.8 m/sec2. Then, what is the distance traveled by the body in the last 0.1 second of its motion?

Q.

Two balls with masses $m_1$ = 3 kg and $m_2$ = 5 kg have initial velocities $v_1$ = 5 m/s = $v_2$ in the directions as shown in figure. They collide at the origin. Find the velocity of the COM 3 seconds before collision?

1. -(12$\hat{i}-15\hat{j}$) m/s

2. (-12 $\hat{i}+15\hat{j}$) m/s

3. (-12 $\hat{i}+15\hat{j}$) m/s

4. (-15 $\hat{i}-12\hat{j}$) m/s

Q. A 30 kg projectile moving horizontally with a velocity ${\overrightarrow{v}}_0=\left(120m/s\right)\hat{i}$ explodes into two fragments A and B of masses 12 kg and 18 kg, respectively. Taking point of explosion as origin and knowing that 3 s later the position of fragment A is (300, 24, –48) m, determine the position of fragment B at the same instant.

1. (400, -91, 48)
2. (360, -91, 48)
3. (360, -45, 32)
4. (400, -91, 32)

Q.

Two bodies A and B of mases m and 2m respectively are placed on a smooth floor. They are connected by a spring. A third body C of mass m moves with velocity $v_0$ along the line joining A and B and collides elastically with A as shown in figure. At a certain instant of time $t_0$ after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be $x_0$. Determine (a) the common velocity of A and B at time $t_0$ and (b) the spring constant.

1. $v=\frac{v_0}{3},k=\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

2. $v=\frac{v_0}{3},k=\frac{3}{4}\frac{m{v}_0^2}{x_0^2}$

3. $v=\frac{v_0}{2},k=\frac{2}{3}\frac{m{v}_0^2}{x_0^2}$

4. $v=\frac{v_0}{2},k=\frac{3}{4}\frac{m{v}_0^2}{x_0^2}$

Q. A block of mass 1 kg is moving down the inclined plane with cons†an t velocity f 10 m/s . if angle of inclination is 37^° then coefficient of kinetic friction between the inclined plane and the block is

Q. A machine gun mounted on a 2000kg car , on a horizontal frictionless surface fires 10 bullets per second . If the mass of each bullet is 10g and 5he velocity of each bullet is 500m/s , then the acceleration of the car will be ?

Q. A bullet of mass 5 gm is fired from a gun of mass 5 kg. What is the velocity of the muzzle if the recoil velocity is 500 m/s?

Q.

A man of mass 'M' having a bag of mass 'm' slips from the roof of a tall building of height 'H' and starts falling vertically (figure). When at a height 'h' from the ground, he notices that the ground below him is pretty hard, but there is a pond at a horizontal distance 'x' from the line of fall. In order to save himself he throws the bag horizontally (with respect to himself) in the direction opposite to the pond. Calculate the minimum horizontal velocity imparted to the bag so that the man lands in the water.

1. 

2. 

3. 

4. 

Q.

A particle of mass m is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is ?

1. $\frac{\pi }{4}+\alpha$

2. $\frac{\pi }{4}$

3. $\frac{\pi }{4}-\alpha$

4. $\frac{\pi }{2}$

Q.

A ball of mass 50 g moving at a speed of 2.0 m/s strikes a plane surface at an angle of incidence ${45}^{\circ }$ . The ball is reflected by the plane at equal angle of reflection with the same speed. Calculate (a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the momentum of the ball.

1. zero, zero

2. 0 zero, 0.14 kg m/s

3. (a)0.14 kg m/s, 0.14 kg m/s

4. 0.14 kg m/s, zero

Q. A person is pulling their luggage by the strap with an applied force at an angle as shown in the diagram.
What is the expression for the normal force acting on the suitcase?

1. Weight
2. Weight $+F_{applied}\sin \theta$
3. Weight $-F_{applied}\cos \theta$
4. Weight $-F_{applied}\sin \theta$
5. Weight $+F_{applied}\cos \theta$

Q.

Light in certain cases may be considered as a stream of particles called "photons". Each photon has a linear momentum $\frac{h}{\lambda }$ where h is the Planck's constant and $\lambda$ is the wavelength of the light. A beam of light of wavelength $\lambda$ is incident on a plane mirror at an angle of incidence $\theta$. Calculate the change in the linear momentum of a photon as the beam is reflected by the mirror.

1. 

2. 

3. 

4. 

Q. State Newton's second law. Prove that Newton's first law of motion is contained in Newton's second law

Q.

A particle moves in the x – y plane under the influence of a force such that its linear momentum is $p\left(t\right)=A\left[\hat{i}cos\right(kt)-\hat{j}sin(kt\left)\right]$, where A and k are constants. The angle between the force and the momentum is

1. $0^{\circ }$

2. ${30}^{\circ }$

3. ${45}^{\circ }$

4. ${90}^{\circ }$